-4x^2+22x-12=0

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Solution for -4x^2+22x-12=0 equation: 


Simplifying
-4x2 + 22x + -12 = 0

Reorder the terms:
-12 + 22x + -4x2 = 0

Solving
-12 + 22x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 11x + -2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-6 + 11x + -2x2)' equal to zero and attempt to solve:

Simplifying
-6 + 11x + -2x2 = 0

Solving
-6 + 11x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
3 + -5.5x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -5.5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -5.5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5.5x + x2 = 0 + -3
-5.5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5.5x + x2 = -3

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = -3 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = -3 + 7.5625

Combine like terms: -3 + 7.5625 = 4.5625
7.5625 + -5.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + -2.75) equal to 2.136000936 and -2.136000936.


Subproblem 1
x + -2.75 = 2.136000936

Simplifying
x + -2.75 = 2.136000936

Reorder the terms:
-2.75 + x = 2.136000936

Solving
-2.75 + x = 2.136000936

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 2.136000936 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 2.136000936 + 2.75
x = 2.136000936 + 2.75

Combine like terms: 2.136000936 + 2.75 = 4.886000936
x = 4.886000936

Simplifying
x = 4.886000936


Subproblem 2
x + -2.75 = -2.136000936

Simplifying
x + -2.75 = -2.136000936

Reorder the terms:
-2.75 + x = -2.136000936

Solving
-2.75 + x = -2.136000936

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -2.136000936 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -2.136000936 + 2.75
x = -2.136000936 + 2.75

Combine like terms: -2.136000936 + 2.75 = 0.613999064
x = 0.613999064

Simplifying
x = 0.613999064


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.886000936, 0.613999064}
Solution
x = {4.886000936, 0.613999064}

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